Syllabus ( MATH 419 )
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Basic information
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Course title: |
Introduction to Coding Theory |
Course code: |
MATH 419 |
Lecturer: |
Assoc. Prof. Dr. Ayten KOÇ
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ECTS credits: |
6 |
GTU credits: |
3 (3+0+0) |
Year, Semester: |
4, Fall |
Level of course: |
First Cycle (Undergraduate) |
Type of course: |
Elective
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Language of instruction: |
English
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Mode of delivery: |
Face to face
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Pre- and co-requisites: |
Math 113 or Math 116 |
Professional practice: |
No |
Purpose of the course: |
The aim of this course is to introduce the basics of coding theory. Morever, it will help students to understand the importance and applications of algebra in real life. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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List the basic notions of coding theory
Contribution to Program Outcomes
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
Method of assessment
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Written exam
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Recognise finite fields, Reed-Solomon codes and use some decoding algorithms of these codes.
Contribution to Program Outcomes
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Being fluent in English to review the literature, present technical projects, and write journal papers.
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Using technology as an efficient tool to understand mathematics and apply it.
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Exhibiting professional and ethical responsibility.
Method of assessment
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Written exam
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Grab cyclic codes and some known bounds for the parameters of codes.
Contribution to Program Outcomes
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Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
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Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
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Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment
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Written exam
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Contents
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Week 1: |
Introduction to error correcting codes. |
Week 2: |
Linear codes. |
Week 3: |
Hamming codes. |
Week 4: |
Introduction to finite fields. |
Week 5: |
Roots of polynomials, primitive elements, field characteristic. |
Week 6: |
Some bounds for the parameters of codes. |
Week 7: |
Reed-Solomon codes and related codes. |
Week 8: |
Decoding algorithms. Midterm Exam. |
Week 9: |
Decoding Reed-Solomon codes using Euclid Algorithm. |
Week 10: |
Minimal polynomial. Cyclotomic cosets. |
Week 11: |
Cyclic codes. |
Week 12: |
BCH codes. |
Week 13: |
BCH bound. |
Week 14: |
Some other bounds for the parameters of codes. |
Week 15*: |
- |
Week 16*: |
Fianl Exam. |
Textbooks and materials: |
R. M. Roth, Introduction to Coding Theory, Cambridge University Press, 2006 |
Recommended readings: |
S. Ling, C. Xing, Coding Theory, A first course, Cambridge University Press, 2004 |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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Method of assessment |
Week number |
Weight (%) |
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Mid-terms: |
8 |
40 |
Other in-term studies: |
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0 |
Project: |
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0 |
Homework: |
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0 |
Quiz: |
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0 |
Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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Courses (Face-to-face teaching): |
3 |
14 |
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Own studies outside class: |
6 |
14 |
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Practice, Recitation: |
0 |
0 |
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Homework: |
0 |
0 |
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Term project: |
0 |
0 |
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Term project presentation: |
0 |
0 |
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Quiz: |
0 |
0 |
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Own study for mid-term exam: |
10 |
1 |
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Mid-term: |
2 |
1 |
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Personal studies for final exam: |
12 |
1 |
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Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)
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